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From the eigenvalue problem theory, we see that the convergence rate of the biharmonic eigenvalues obtained by the mixed method in I. Bab u ˇ ska and J. Osborn, [Eigenvalue Problems, Handbook of Numerical Analysis, Vol. II, North-Holland, Amsterdam, 1991.] is h 2 k − 2 for k ≥ 2. In this paper, we give a presentation of the lowest-order virtual element method for the approximation of Kirchhoff plate vibration problem. This discrete scheme is based on a conforming H 1 (Ω) × H 1 (Ω) formulation, following the variational formulation of Ciarlet–Raviart method, which allows us to make use of simpler and lower-regularity virtual element space. By using the classical spectral approximation theory in functional analysis, we prove the spectral approximation and optimal convergence order h 2 for the eigenvalues. Finally, some numerical experiments are presented, which show that the proposed numerical scheme can achieve the optimal convergence order. [ABSTRACT FROM AUTHOR]

In this paper we consider rational approximation of functions in the Hardy spaces on the strip with . Observing that can be regarded as the direct sum of and , we give three kinds of adaptive rational approximation in enhancing the corresponding approximations in and where and We also obtain a type of approximation for subspaces in by making use of Riesz bases in these subspaces. [ABSTRACT FROM AUTHOR]

In this paper, it is shown that the necessary conditions for stability of Kharitonov polynomials can be checked by simply inspecting few upper and lower bound coefficients. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of a micropolar fluid flowing past a stretching surface involving both heat and mass transfer with Ohmic heating and viscous dissipation. A similarity transformation is employed to change the governing equations into nonlinear coupled higher-order ordinary differential equations. These equations are solved numerically using a finite element method with linear shape functions and a Chebyshev finite difference method that involves higher-order polynomials. Numerical results of both methods have been compared with the closed-form solution of a particular case when the material parameter is taken to be zero. Good agreement between the numerical results of both methods, together with excellent agreement with the closed-form solution, ensures the reliability of using linear shape functions in the finite element method. The effect of the parameters governing the problem on the velocity, microrotation, temperature and concentration functions has been studied for different boundary conditions. [ABSTRACT FROM AUTHOR]

This paper proposes the use of approximate posterior distributions resulting from operational prior distributions chosen with regard to the realized likelihood function. L.J. Savage's "precise measurement" is generalized for approximation in terms of an arbitrary operational prior density, including mixed-type prior distributions with positive probabilities on singular subsets. A new approximation is also given relating such distributions to absolutely continuous distributions with high local concentrations of density, Mixed-type distributions constructed from the natural conjugate prior distributions are proposed and illustrated in the normal-sampling case for unified Bayesian inference in testing and estimation contexts. [ABSTRACT FROM AUTHOR]